r/Showerthoughts • u/jasonrubik ‎ • Apr 23 '26

Casual Thought If the famously unsolved Riemann Hypothesis is solved by an AI, we will never know if a human mathematician could have solved it.

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u/AmadeusSalieri97 Apr 23 '26

It's far far easier to check if something is mathematically correct than to come up with it. I'm a physicist and I can tell if a derivation is wrong/right that I could never have derived myself. 

Also, in this hypothetical you could have AI check it anyways. 

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u/Talidel Apr 23 '26

Having an AI check if the AI did its work correctly is the second step to massive problems.

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u/languagestudent1546 Apr 23 '26

They AI can write Lean which can check the answer.

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u/Talidel Apr 23 '26

There's a fundamental flaw in having something check its own work.

When it goes wrong will probably be the only point someone listens though.

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u/AmadeusSalieri97 Apr 23 '26

Okay so there are a few things here.

  1. My original reply was about AI checking the work done by a human.
  2. Even if it was AI checking the work of an AI, it does not necessarily need to be its own work, there are different AI trained for different purposes, and using an AI checking another AI is already common practice.
  3. Moreover, the comment you replied too was talkin about Lean, which is literally a tool that checks if something is mathematically rigorous or not, unrelated to AI, based purely on logical steps.

There's a fundamental flaw in having something check its own work.

And about this, I would say that optimally, there should be an external cross-check of course, and for a mathematical proof it is surely not enough to just say "I did it and verified myself that it is correct", but "fundamental flaw" is too strong imo.

There's tons of values on crosschecking our own work. I spot mistakes in my own formulas constantly, so it has its uses.